Finite Group Databasebeta

C2×#117×D23 #15686559

order2944
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#117×D23

Splittings

FittingC2×C23×#117 ⋊ C2
SylowC23 ⋊ C22×#117

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutatorC2×C23C24×C4
FrattiniC22C24×D23
FittingC2×C23×#117C2
socleC23×C23C24
prime radicalC24×D23C22
cosocleC22×C23C25
hypercenterC2×#117D23
hypocenterC23C22×#117
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×#117

1880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17672);